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立方体的旋转对称

立方体的旋转对称
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2018-01-17 16:27
立体几何变换几何作图
这个范例演示了立方体的旋转对称性。核心数学概念包括旋转对称和立体几何。通过使用GeoGebra命令如Cube、PointIn、Line、Rotate、Midpoint等，可以构造立方体及其旋转对称图形。适合初中及以上学生学习立体几何和对称性。

GeoGebra 命令及参数

  1. Cube(H, E, xOyPlane) → a, F, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, G, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH, C, D, A, B, faceABCD, faceADHE, faceABFE
  2. PointIn(faceABCD) → J
  3. PointIn(faceEFGH) → I
  4. Line(I, J) → b
  5. Rotate(a, (-α), b) → a'
  6. Rotate(faceABCD, (-α), b) → faceABCD'
  7. Rotate(faceABFE, (-α), b) → faceABFE'
  8. Rotate(faceADHE, (-α), b) → faceADHE'
  9. Rotate(faceBCGF, (-α), b) → faceBCGF'
  10. Rotate(faceCDHG, (-α), b) → faceCDHG'
  11. Rotate(faceEFGH, (-α), b) → faceEFGH'
  12. Midpoint(D, B) → K
  13. Midpoint(H, F) → L
  14. Midpoint(edgeFG) → Q
  15. Midpoint(edgeGH) → R
  16. Midpoint(edgeEH) → S
  17. Midpoint(edgeEF) → T
  18. Midpoint(edgeBC) → W
  19. Midpoint(edgeAD) → B_1
  20. Midpoint(edgeAB) → C_1
  21. Midpoint(edgeCD) → D_1